'Divine' or 'Golden' Arterial Pulse

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Vatican Palace, Rome, 1509 [Source: Wikimedia Commons, the free media repo- sitory] .... the same level of excellence, incredible work ethic and joie de vivre.
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body is about to appoint its first woman President in 60 years. ‘Scientific and professional societies can do a lot to educate the community by letting women know that they will be given equal consideration when leadership positions come up and by informing men that gender balance is normal and acceptable. It’s happened in politics with more women taking leadership roles, now medicine needs to catch up with this’. Along with other senior women in cardiology, she can sense a seachange with more women coming into medical school and outperforming their male peers. These numbers have still not filtered through to senior positions yet, and Priori suggests that there may be a residual reluctance to appoint a woman to a senior position in competition with a male colleague. While women lack the networks that men build very successfully, they have a capacity for multi-tasking that is invaluable in a clinical environment. When it comes to emotional intelligence and relationship building women also tend to be more advanced than their male peers. They tend to talk and interact better with patients and build better relationships using softer skills. She advises young women to arm themselves for a career in clinical medicine and be prepared for the challenges. ‘Even if you are smart

and motivated you need to be prepared for the difficulties that lie ahead. This applies to young men as much as it applies to young women because it’s tough. Women need to stand up for themselves and offer to help rather than wait around for someone to ask them. A lot of women’s mentality in this respect goes back to their early education and being told to be quiet and not wanting to be seen as pushy or aggressive. It can take a while and require a lot of support to help women overcome this. I still receive calls from some of my former female PhD students four or five years after they’ve finished working with me. They often ask me for help and advice about the next steps they should take or asking for advice about how to balance their career and it’s a great thing to be able to see them developing’

Judy Ozkan MA [email protected]

Conflict of interest: none declared.

doi:10.1093/eurheartj/ehx542

The ‘Divine’ or ‘Golden’ Arterial Pulse Scholars suggest an alternative method of characterizing the pulse based on ancient Greek descriptions By the Hellenistic period, the Greeks had presided over one of the most dramatic and significant revolutions in mathematical science of all time, having adapted and adopted important knowledge from the Babylonians and the Egyptians. Among many fundamental concepts and theories developed and established during those times there is one unit with remarkable properties and applications; the Golden Ratio (as known today), or otherwise called Divine Proportion, Extreme and Mean Ratio, and Golden Section or Golden Number. This unit is defined as the ratio of two quantities (a and b) where the ratio of the sum of the quantities (a þ b) to the larger quantity (a) equals the ratio of the larger quantity (a) to the smaller one (b). The respective equation form is: a/b ¼ (a þ b)/a def / where / is ¼ the golden number 1.6180339887498948420 which is usually rounded to 1.618. There are several mysterious and fascinating properties of the Golden Ratio which are not only applicable to mathematics but also to biology, medicine, art, nature, music, architecture, psychology, aesthetics, theology, and other fields. According to the astrophysicist Mario Livio (1945–present), the Golden Ratio has inspired thinkers of all disciplines like no other number in the history of mathematics. The roots of the Golden Ratio concept are very difficult to accurately locate back in time. It appears that the Egyptians may have used / in the design of the Great Pyramids, 2560 BC. Nevertheless, most evidence indicates that the mathematical concept of this number was

theoretically described by the mathematician and philosopher Pythagoras of Samos (ca 580BC–500BC) and his School. The mathematician Euclid of Alexandria (mid-4th century–mid3rd century BC) did a more systematic description of the ‘extreme and mean ratio’ as written in his work The Elements, which remains one of the most influential works in the history of mathematics. Euclid’s elements provide the first known written definition of what is now called the Golden Ratio: ‘A straight line is said to have been cut in extreme and mean ratio when, as the whole line is to the greater segment, so is the greater to the lesser’. However, it is also believed that Euclid does not present original work about this ratio; some attribute the material to the studies by Theodorus of Cyrene (465– 398 BC) while others to Pythagoras, or at least to the Pythagoreans.1 Until now, this ratio is denoted by the Greek letter / (phi), honouring the name of the Greek sculptor, painter, and architect Phidias (480–430 BC), who is said to have employed it extensively in his sculptures including those of the Parthenon. The Golden Ratio has been observed and applied in several biological and medical fields, whereas few publications have highlighted its appearance and applicability in the cardiovascular (CV) system.2,3 Nonetheless, limited evidence exists that the arterial pulse exhibits characteristics that approximate the Golden Ratio. Thus, an intriguing and novel philosophical and mathematical question is the following; are there any ‘divine’ or ‘golden’ arterial pulse waves whose peak values fulfil the golden ratio both in the vertical (pressure scale) and

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Figure 1 Key figures in the history of the mean and extreme ratio or golden ratio / (phi). (A) Detail of Pythagoras with a tablet of ratios, numbers sacred to the Pythagoreans, from The School of Athens by Raphael. Vatican Palace, Rome, 1509 [Source: Wikimedia Commons, the free media repository], (B) Euclid of Alexandria [Source: Wellcome Library, London], and (C) Leonardo Fibonacci (c. 1175–c. 1250), Italian mathematician who introduced Europe to the Fibonacci sequence that incorporates the golden number [Source: www. it.wikipedia.org].

Figure 2 A fragment of the second book of the Elements of Euclid in Greek, discovered in 1897 at Oxyrhynchus, Egypt. Illustration by Jitse Niesen, uploaded by Cristian Violatti, published on 13 June 2013. Licence: http://www.ancient.eu/image/1280/.

horizontal axis (time scale)? Herein we propose that the arterial pulse can be analysed according to the scheme illustrated in Figure 3. Specifically, blood pressure levels, namely, the minimum (diastolic blood pressure; DBP), the pulse height (pulse pressure; PP), and the maximum (systolic blood pressure; SBP) as well as the diastolic duration (DD), ejection duration (ED) and cardiac period can be expressed by three lines a, b, and a þ b respectively, similar to the

lines described by the Pythagoreans. Theoretically, the ‘divine’ or ‘golden’ pressure and time points of an arterial pulse should follow the golden ratio / (phi) according to the equation: a aþb DD Period DBP SBP ¼ def ¼ / or ¼ ¼ ¼ def b a ED DD PP DBP ¼ / where /  1.618.

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Figure 3 The ‘Divine’ or ‘Golden’ arterial pulse model according to the golden ratio / (phi).

In this respect for any given SBP there is a single DBP that fulfils the above conditions and vice versa. Also for any given cardiac period (heart rate) there is a single ED or DD which provides ratios equal to the golden number 1.618. For example, the normal values of brachial SBP/DBP that currently exist, i.e. 120/80 mmHg respectively, correspond to the ratios DBP/PP ¼ 2 and SBP/DBP ¼ 1.5. It is obvious that under specific CV and autonomic nervous system conditions two explicit SBP/DBP values can provide proportions equal to the golden number / (such as SBP/DBP ¼ 120/74.16 mmHg  1.618). In an analogous perspective, the duration of the whole pulse (namely the cardiac period), the ED and DD may exhibit under circumstances ratios that equal to / (phi). For example, for a heart rate 80 beats per minute (period ¼ 0.750 s), an ED 0.29 s and a DD 0.46 s exhibit the divine proportions. The arterial pulse has been studied from ancient years until today with the main purpose to distinguish abnormalities related to health problems or to detect early signs predisposing to CV risk. For centuries scientists have been exploring the pathophysiological characteristics of the arterial pulse. After the fundamental developments of Scipione Riva-Rocci (1896–1937) and Nikolai-Sergeyevich Korotkov (1874–1920) who set the foundation for the non-invasive, cuff-based, measurement of BP levels at the brachial artery,4 a great number of clinical and epidemiological studies have provided a huge amount of data which have been used to determine, the ‘normal’ values of SBP and DBP. Thus, until now the optimum height and level of the arterial pulse on the scale of mmHg has been defined statistically based on clinical, evidence based observations using BP recordings only at the brachial artery. Nevertheless, during the last three decades several technological innovations and advances have provided tools to assess BP: i. at different arterial sites focusing mainly on the central arteries (aorta and carotid) which are closer to target organs (heart and brain) than the brachial artery,5,6

ii. at different time points either within the same day (by ambulatory BP monitoring) or at different longer time intervals7 (i.e. by home monitoring or telemonitoring).

As our understanding of blood flow and arterial pathophysiology has advanced in parallel to the development of new technologies, a ‘spatio-temporal’ approach in BP assessment is more and more for consideration.8 This concept denotes that the classic measurement of BP at the brachial artery (and its corresponding BP values) does not always provide the maximum information for CV risk assessment, because these values do not necessarily reproduce the average BP of an individual exposed to different conditions and neither reflects the central BP values that regulate target organ functions such as the heart and the brain. Therefore, a great challenge is to detect which arterial pulse(s) among the plethora of various arterial pressure waveforms which vary (i) along the arterial tree, (ii) over time, and (iii) among individuals or due to other conditions, has (have) the maximum and the most accurate clinical relevance? According to Pythagoras ‘First of all is number’. Whether the arterial pulse analysed by the proposed philosophical and mathematical approach has any potential physical and clinical relevance remains to be further explored. Theodore G. Papaioannou1*, Elias Gialafos2, Marianna Karamanou3, Gregory Tsoucalas4, Dimitris Tousoulis1 1

Biomedical Engineering Unit, First Department of Cardiology, Medical School, National and Kapodistrian University of Athens, Athens, Greece; 2Eginitio Hospital, Medical School, National and Kapodistrian University of Athens, Athens, Greece; 3University Institute of History of Medicine and Public Health, University of Lausanne, Lausanne, Switzerland; 4Institute for the History of Medicine, School of Medicine, University Claude Bernard, Lyon, France.

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2928 *Correspondence Theodore Papaioannou Biomedical Engineering Unit, 1st University Department of Cardiology, Hippokration Hospital, Vas. Sophias 114, Athens 115 27, Greece. Tel: 0030 213 2088286, Fax: 0030 213 2088676, e-mail: [email protected]

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Conflict of interest: None declared.

References References are available as supplementary material at European Heart Journal online.

The order of authors’ names accords to their contribution.

doi:10.1093/eurheartj/ehx543

Obituary

Daniel R Wagner: An appreciation Daniel Wagner MD PhD 29 May 1963–5 July 2017 is remembered by friends and colleagues from both sides of the Atlantic

It is with great sadness that the cardiology community learned of the untimely death of Daniel Wagner recently. Daniel was a superb interventional cardiologist and academic who had trained and practised in the US, Germany, Belgium, Luxembourg, and more recently Switzerland. He had graduated from the University of Giessen in Medicine in 1990. A major step in Daniel’s career was when he went to the University of Pittsburgh School of Medicine and the University of Pittsburgh Medical Center in July 1994. Daniel had been recruited by the late Dr James Shaver to serve as a Fellow in Cardiology, while his wife Kerstin trained in paediatric cardiology at the Children’s Hospital of Pittsburgh. Daniel stood out amongst a highly talented group of Fellows. He was a superb clinician who demonstrated outstanding diagnostic skills at the bedside, exceptional technical skills, a compassion for patients and an infectious enthusiasm no matter the challenge or the undertaking. His technical skills led him to subsequent training in interventional cardiology, though he could have readily pursued any of the sub-specialities of cardiology. But Daniel also excelled in the basic science laboratory. He joined the laboratory of Arthur Feldman, the newly arrived Chief of

Cardiology, where he was able to continue his long-standing interest in adenosine. However, he applied it to a new area of research—the pro-inflammatory cytokines. In a series of seminal studies, he demonstrated that adenosine had a potent effect on regulating the expression of pro-inflammatory cytokines in isolated cardiac cells as well as in the failing human heart. These studies, which have stood the passage of time, set the stage for future work in cardiac cytokines and were the substance of his doctoral thesis. In the lab, Daniel showed the same level of excellence, incredible work ethic and joie de vivre that characterized his time on the clinical service. His enthusiasm and dedication were infectious, and he made everyone in the laboratory, students and post-docs alike, more productive. Furthermore, Daniel’s time in Pittsburgh established what would be a life-time collaboration and friendship with his mentor even as their interests transitioned to other areas. In 1999, Daniel moved back to his native Luxembourg to take up a position in the Centre Hospitalier Luxembourg as an Interventional Cardiologist. Though advised by Arthur Feldman that you cannot do basic science and be an interventional cardiologist—Daniel did not

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